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A wooden cylinder of length L is partly ...

A wooden cylinder of length L is partly submerged in a liquid of specific gravity `rho_(1)` with `n^(th)` `(nlt1)` part of it inside the liquid. Another immiscible liquid of density `rho_(2)` is poured to completely submerge the cylinder. Density of cylinder `rho` is the geometric mean of the densities of the two liquid.
Calculate the fraction of the cylinder submerged in the lower liquid after the upper liquid is poured in the vessel

A

`(1-x_2)/(x_1-x_2)`

B

`(1-x_1)/(x_1+x_2)`

C

`(x_1-x_2)/(x_1+x_2)`

D

`(x_2)/(x_1)-1`

Text Solution

Verified by Experts

The correct Answer is:
A
`rho_1 x_1 g=rho_1 x_2 g+rho_2(1-x_2)g`
`implies (rho_1)/(rho_2)=(1-x_2)/(x_1-x_2)`.
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